Methods and systems for measurement and estimation of normalized contrast in infrared thermography

ABSTRACT

Methods and systems for converting an image contrast evolution of an object to a temperature contrast evolution and vice versa are disclosed, including methods for assessing an emissivity of the object; calculating an afterglow heat flux evolution; calculating a measurement region of interest temperature change; calculating a reference region of interest temperature change; calculating a reflection temperature change; calculating the image contrast evolution or the temperature contrast evolution; and converting the image contrast evolution to the temperature contrast evolution or vice versa, respectively.

I. CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of the filing date of U.S.provisional patent application No. 61/293,426 incorporated herein byreference, which was filed on Jan. 8, 2010 by the same inventor of thisapplication.

II. ORIGIN OF THE INVENTION

The invention described herein was made by an employee of the UnitedStates Government and may be manufactured and used by or for theGovernment of the United States of America for governmental purposeswithout the payment of any royalties thereon or therefor.

III. FIELD OF THE INVENTION

The invention is directed to the fields of non-destructive evaluation(NDE) and of processing of data acquired from an infrared camera.Specifically, the systems and methods described herein concern theperformance of a series of steps for analyzing and processing digitaldata comprising a plurality of infra-red (IR) video images acquired by asystem used for non-destructive evaluation.

IV. BACKGROUND OF THE INVENTION

The embodiments described herein relate generally to the field ofnon-destructive evaluation (NDE) using thermographic images. Infrared(IR) flash (or pulsed) thermography is an example of a technique for NDEused in the inspection of thin materials such as laminated or bondedcomposites in the aerospace industry. IR flash thermography is used todetect delamination-like anomalies, although other anomalies, such assurface cracks, may be detected.

An example of hardware equipment for an IR flash thermography systemcomprises a flash lamp (source of light/heat), a flash hood or housing,a flash power supply/trigger unit, a flash duration controller, an IRcamera for capturing video images, data acquisition electronics, and acomputer. The computer may be used for controlling the flash trigger,for acquiring video data from the IR camera, for displaying data, andfor post-processing of the acquired data.

In one example of an NDE technique using IR flash thermography, a singlesided or reflection technique is used wherein the flash lamp (heatsource) and the IR camera (detector) are on the same side of a testobject undergoing inspection. A plate is provided as the test objectwith a round delamination in the center. After applying heat to the topsurface of the test object by triggering the flash lamp, the top surfacearea surrounding the anomaly cools faster than the top surface(footprint) area above the anomaly. The IR camera captures a sequence ofimages of the surface temperature in terms of pixel intensity andrepresents the anomaly as a hot spot (e.g., an area warmer than thesurrounding area or the reference region of interest (ROI)). The hotspot is about the size and shape of the anomaly footprint. Relativepixel intensity, i.e., the difference in pixel intensity between the hotspot (measurement ROI) and the surrounding area (reference ROI), varieswith the post-flash time. Deeper anomalies appear in the IR video dataat later times compared to the near surface anomalies. After the initialappearance of an anomaly in the IR video data, the relative pixelintensity continues to increase with time. The relative pixel intensityof the anomaly reaches a peak at a certain time, and then the relativepixel intensity decays until the temperature of the indication area andthe temperature of the surrounding area become equal.

V. SUMMARY

In one aspect, disclosed is a method for converting an image contrastevolution of an object to a temperature contrast evolution, the methodcomprising: calculating a measurement region of interest temperaturechange ΔT; calculating a reference region of interest temperature changeΔT_(ref), calculating a reflection temperature change ΔT_(refl);calculating the image contrast evolution C _(W) ^(l); and converting,using a processor, the image contrast evolution to the temperaturecontrast evolution.

In another aspect, disclosed is a method for converting a temperaturecontrast evolution of an object to an image contrast evolution, themethod comprising: calculating a measurement region of interesttemperature change ΔT; calculating a reference region of interesttemperature change ΔT_(ref); calculating a reflection temperature changeΔT_(refl); calculating the temperature contrast evolution C ^(l); andconverting the temperature contrast evolution to the image contrastevolution.

In another aspect, disclosed is an apparatus for converting an imagecontrast evolution of an object to a temperature contrast evolution, theapparatus comprising one or more processors and one or more memory unitscoupled to the processors. The apparatus is configured and arranged tocalculate a measurement region of interest temperature change ΔT, tocalculate a reference region of interest temperature change ΔT_(ref), tocalculate a reflection temperature change ΔT_(refl), to calculate theimage contrast evolution C _(W) ^(l), and to convert the image contrastevolution to the temperature contrast evolution.

In another aspect, disclosed is an apparatus for converting atemperature contrast evolution of an object to an image contrastevolution, the apparatus comprising one or more processors and one ormore memory units coupled to the processors. The apparatus is configuredto: calculate a measurement region of interest temperature change ΔT;calculate a reference region of interest temperature change ΔT_(ref);calculate a reflection temperature change ΔT_(refl); calculate thetemperature contrast evolution C ^(l); and convert the temperaturecontrast evolution to the image contrast evolution.

In another aspect, disclosed is a method for assessing emissivity of anobject being inspected by an infrared flash thermography system, themethod comprising the steps of: measuring a pre-flash temperature at ameasurement region of interest W⁰; calculating a camera constantC_(cam); and calculating the emissivity of the object according to theequation of:

$ɛ \cong {\frac{\frac{W^{0}}{B} - J}{1 - J}.}$

In yet another aspect, disclosed is a method for calculating anafterglow heat flux evolution S_(postflash), the method comprising thesteps of measuring a reflection temperature T_(refl); and calculatingthe afterglow heat flux evolution S_(postflash) according to theequation of:S_(postflash)=σ(T_(refl) ⁴−T_(refl) ⁰ ⁴ ),wherein T_(refl) ⁰ is the reflection temperature at time of flash and σis the Stefan-Boltzmann Constant.

VI. BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of an exemplary single-sided flashthermography system in accordance with some embodiments describedherein.

FIGS. 2( a) and (b) are a schematic diagram of a plate depicting agapping delamination with measurement and reference regions of interest(ROIs) and a single infrared (IR) video image of a test object with backdrilled flat bottom holes, respectively, in accordance with someembodiments described herein.

FIG. 3 is an infrared image of a plate with back drilled flat bottomslots along with foils and tape (post-flash time=0.6 sec), in accordancewith some embodiments described herein.

FIG. 4 is a graph of the value of pixel intensity as a function ofposition along a horizontal cross line in a frame taken at 0.6 secondsafter the flash, in accordance with some embodiments described herein.

FIG. 5 is a graph of the pixel intensity evolution as a function of timeon the foil ROI (lower evolution from the left foil ROI and upperevolution from the right foil ROI) with the peak time of 0.6 secondsindicated by the dashed vertical line, in accordance with someembodiments described herein.

FIG. 6 is a graph of the pixel intensity evolution as a function of timefor the tape ROI, in accordance with some embodiments described herein.

FIG. 7 is a graph of the ROI intensity evolutions for the measurement(upper evolution) ROI and the reference (lower evolution) ROI, inaccordance with some embodiments described herein.

FIG. 8 is a graph of simple contrast evolution at the measurement ROIwith the peak time of 0.5 seconds indicated by the dashed vertical line,in accordance with some embodiments described herein.

FIG. 9 is a graph of computed evolution of the reflection temperature,in accordance with some embodiments described herein.

FIG. 10 is a graph of estimated temperature evolutions for themeasurement ROI (middle curve), the reference ROI (bottom curve). andthe reflection or the background ROI (top curve), in accordance withsome embodiments described herein.

FIG. 11( a) is a graph of normalized image contrast computed using thepixel intensity (upper curve) and one fourth power of the pixelintensity, in accordance with some embodiments described herein.

FIG. 11( b) is a graph of measured normalized image contrast (lowercurve) and estimated normalized temperature contrast (upper curve), inaccordance with embodiments described herein.

FIG. 12 is an exemplary screen shot displaying normalized temperaturecontrast evolution (upper curve) and normalized image contrast evolution(lower curve) computed using software that implements simulation anddata analysis methods described herein in accordance with someembodiments.

FIG. 13 is a graph of the pixel intensity to temperature contrast ratio,in accordance with some embodiments described herein.

FIG. 14 is a graph of simulated temperature evolutions with an assumedreflection temperature evolution, in accordance with some embodimentsdescribed herein.

FIG. 15 is a graph of estimated image contrast and of simulatedtemperature contrast, in accordance with some embodiments describedherein.

FIG. 16 is a graph of estimated afterglow flux as a function of timecharted from the first post-flash frame, in accordance with someembodiments described herein.

FIG. 17 is a graph of flash flux evolution as a function of time untilthe first post-flash frame, in accordance with some embodimentsdescribed herein.

FIG. 18 is a flow diagram illustrating methods for converting an imagecontrast evolution of an object to a temperature contrast evolution, formodeling afterglow flux, and for assessing the test object emissivity,in accordance with some embodiments described herein.

FIG. 19 is a flow diagram illustrating a method for converting atemperature contrast evolution of an object to an image contrastevolution, in accordance with some embodiments.

Because the embodiments described herein are subject to variousmodifications and alternative forms, it should be understood that thedrawings and detailed description are not intended to limit theinvention to the particular embodiments described herein. Instead, thefollowing description is intended to cover all modifications,alternatives, and equivalents falling within the scope of the inventionas defined by the appended claims.

VII. DETAILED DESCRIPTION

The objects in the drawings are not necessarily to scale and certainfeatures may be shown exaggerated in scale or in somewhat generalized orschematic form in the interest of clarity and conciseness. In thedescription which follows like parts may be identified throughout thespecification and drawings with the same reference numerals. Theforegoing brief description of the drawings is provided for a morecomplete understanding thereof. It should be understood, however, thatthe embodiments described herein are not limited to the precisearrangements and configurations shown. Although the design and use ofvarious embodiments are discussed in detail below, it should beappreciated that the embodiments described represent concepts that maybe embodied in a wide variety of contexts. The specific aspects andembodiments described herein are merely illustrative, for it would beimpossible or impractical to include all of the possible embodiments andcontexts in this description of the invention. Upon reading thisdescription, alternative embodiments will be apparent to persons ofordinary skill in the art.

During the processing of digital data acquired from an infrared camera,normalized image (or pixel intensity) contrast and normalizedtemperature contrast differ in value for objects having a value ofemissivity other than one. Therefore, for more accurate processing ofdata obtained from objects having an emissivity value other than one,the two quantities should not be treated as the same. In the co-pendingU.S. patent application Ser. No. 12/900,644, filed Oct. 8, 2010 andentitled “Methods and Systems for Characterization of an Anomaly UsingInfrared Flash Thermography”, which is hereby incorporated in itsentirety by reference, Koshti distinguishes and defines the twoquantities of normalized pixel intensity contrast and normalizedtemperature contrast. Embodiments described herein establish formulas toestimate the normalized temperature contrast from the normalized pixelintensity or image contrast using the methods and systems describedherein. The method includes steps for the measurement of the reflectiontemperature evolution by comparing the simulation temperature contrastwith the measured pixel intensity contrast. The method also comprisesthe act of estimating the incident heat flux. Ideally, the simulationshould model the compound heat source flux evolution which also includesthe thermal afterglow. The effect of the reflection temperature in thepixel intensity should also be accounted for to seek a more refinedestimation of the temperature contrast profile from the pixel intensityevolution data.

The method of measuring reflection temperature evolution is describedherein. First, the reflection temperature evolution is established basedon infrared (IR) flash thermography (or simply any transientthermography) data acquisition. This acquisition of data requires a testobject, a high emissivity tape with known emissivity, and a diffused buthighly reflective metal foil with known reflectivity. The method alsorecords the steady state pre-flash temperature of the object using athey thermocouple (or other contact sensor) or an accurate radiometer.The IR datacube is recorded after performing the technique of IR flashthermography.

The method further comprises data acquisition from four regions ofinterests (ROI). One region is for the measurement area. The second ROIis for the reference area. The third ROI is for the measurement of thereflection temperature. The fourth ROI is for the measurement of thepre-flash temperature of the high emissivity tape.

Using formulas given herein, the method estimates the reflectiontemperature evolution. Then, the method computes the temperaturecontrast from the IR data. The emissivity factor is defined to relatethe temperature contrast to the image contrast.

The method uses the reflection temperature evolution to model theafterglow flux of the flash source. Using the estimated compound sourceevolution in the simulation software, the method can estimate thetemperature contrast evolutions and then estimate the image contrastprofiles on simulated voids.

The invention provides an emissivity estimation technique using the sameIR camera. The technique estimates the emissivity of an object for adesired thermal wavelength. It is shown that using the foil-tape (ortape-foil) technique during the IR shot, the transient reflectiontemperature or the reflection temperature evolution can be recorded. Ifthe IR camera is programmed to use the real-time reflection temperatureusing the formulas described herein, it can provide real-time objectsurface temperature. The IR camera can be programmed to estimate theobject emissivity in real-time using the formulas derived herein for thefoil-tape technique.

Referring now to the drawings, FIG. 1 is a schematic diagram of anexemplary single-sided flash thermography system in accordance with someembodiments described herein. As shown in FIG. 1, the equipment for aninfrared (IR) flash thermography (IRFT) system 105 in accordance with atleast one of the exemplary embodiments described herein comprises aflash lamp (source of light/heat) 110, a flash-hood 115, at least oneflash power supply/trigger unit 120, at least one flash durationcontroller 125, an IR camera 130 for capturing video images, camera dataacquisition electronics 135, and a computer 140. The computer 140 isused for controlling the flash trigger unit 120 for powering the flashlamp 110, data acquisition of the camera video data, data display, andpost processing of the acquired data. The flash-hood 115 may be madefrom sheet metal and have highly reflective (ε=0.05) inside wallsurfaces. The flash-hood may form a box-like structure, although otherstructures that form an interior volume, such as a cylinder,hemi-sphere, etc. may also be used. However the flash-hood isstructurally configured, one portion of the hood has a large opening soas to enable the hood to be positioned over a test object 145. The sideopposite to the opening has a hole in the center to provide a window forthe lens of the IR camera 130 that is positioned outside of theflash-hood 115. The IR camera 130 is focused at a surface of the testobject 145 positioned within the hood. At least one flash lamp 110 (twoare shown in FIG. 1) is located within the inner wall of the flash-hood115 in proximity to the IR camera 130. The flash lamp(s) 110 is coveredwith a glass shield which is highly transmissive for light but highlyemissive for thermal radiation. The flash lamp(s) 110 when powereddirects illumination towards the test object 145 without directlyshining light upon or into the IR camera 130. The flash-hood 115functions as a housing that contains most of the intense flash from theflash lamp 110.

If the size of the test object 145 can be accommodated inside the hood115, then the test object 145 is located at the hood opening or slightlyinside the hood 115. Otherwise, the test object 145 is located slightlyoutside of the hood 115 opening. A short duration (e.g. 3 millisecond),intense (12 kJ) flash is triggered by the computer 140. Data acquisitionis initiated a few seconds before the flash, and it continues until aprescribed duration of time has expired. The camera 130 provides asequence of IR images (or frames) called the data-cube (or digitalvideo) of the test object surface taken at the chosen frame rate (e.g.60 Hz or 60 frames per see). As described in further detail herein, theintensity (numerical value) of each pixel of the image is a function ofthe surface temperature of the corresponding area observed of the testobject 145 at the time of the image frame. The flash causes the surfaceof the test object 145 to warm up slightly, and the heat then starts todissipate rapidly. The surface cools through thermal radiation,convection, and conduction. Heat conduction within the test object 145is considered to be the dominant heat transfer mode until thetemperature gradients within the test object become small. At latertimes, the heat conduction is of the order of the combined effect ofheat convection and radiation. The IR data acquisition and data analysisutilizes the thermal data in the short duration immediately after theflash where the thermal dissipation is dominated by the heat conductionwithin the test object 145.

Heat exchange across the boundaries due to convection can be assumed tobe zero if the Biot number (N_(Bi)=hL/k) is less than 0.1. For example,a half centimeter thick graphite/epoxy (k=0.64 W/mK) plate, using h=10W/m²K, has a Biot number of 0.078. Therefore, heat conduction is thedominant mode of heat transfer in this graphite/epoxy plate example.Thinner test objects tend to equalize the temperature within the testobject very quickly and have a relatively longer cooling time by heatloss to environment.

FIG. 2( a) is a schematic diagram of a plate serving as the test object145. FIG. 2( a) depicts a gapping delamination or anomaly 220 withmeasurement and reference regions of interest (ROIs) in accordance withembodiments described herein. FIG. 2( b) shows a single infrared (IR)video image of a test object with a flat bottom hole in accordance withat least one embodiment. Referring now to FIGS. 1 and 2( a), the testobject 145 is made of a thermally isotropic material with constantthickness 205 that fits inside the hood 115. The test object 145 issupported at the corners on insulating standoffs 150 and the hood isoriented vertically thereabove. Assuming that the flash intensity isuniform over the test object top surface 210, the heat conduction willbe in a direction normal to the test object top surface 210 in most ofthe acreage area (i.e., area away from edges of the test object andflash boundary). The heat is conducted uniformly from the top surface ofthe test object 210 to the bottom surface of the test object 215. Normalheat conduction will be obstructed by an anomaly such as a small roundgapping delamination 220 at the center of the test object, as depictedin FIG. 2( a). The delamination 220 is at some depth (d) 221 below thetop surface of the test object 210. The delamination may also becharacterized as having some diameter (D) or width 222 and a gap 223.The volume hounded by the anomaly 220 on one side and the top surface210 on the other side is called the heat trapping volume 225.

The top surface area 230 surrounding the anomaly 220 cools faster thanthe top surface (footprint) area 235 above the anomaly 220. The IRcamera 130 captures the surface temperature image in terms of the pixelintensity and shows the anomaly 220 as a hot spot (e.g. an area warmerthan the surrounding area) which is about the size and shape of theanomaly footprint. The relative pixel intensity of the hot spot changeswith the time. Deeper anomalies appear at later times in the IR videocompared to the near surface anomalies. After the appearance of ananomaly in the IR video, its relative pixel intensity continues toincrease with time. The relative pixel intensity associated with theanomaly reaches a peak at a certain time, and then the relativeintensity decays until the indication area temperature and thesurrounding area temperature become equal.

FIG. 2( b) shows one of the frames in a sample IR data-cube from areinforced carbon-carbon (RCC) part with round flat bottom holes (FBHs)machined into the back surface to simulate gapping delaminations ofdiffering depths. IR indications 240 from different flat bottom holesare clearly visible in the IR image. A measurement ROI 245 is shown as asquare in the middle of one of the anomalies. A reference ROI 250 isshown as a square outside the anomaly area. As the test concludes, thetest object continues to cool down to ambient temperature through heatconvection and radiation.

In some embodiments, such as for a test object that is a flat plate witha large diameter, the top surface may be represented as being at atemperature T₁ and similarly the bottom surface is at a temperature T₂.A heat conduction rate for an isotropic slab may accordingly be given byequations (1) and (2),

$\begin{matrix}{q_{k} = {\frac{T_{1} - T_{2}}{\left( {{L/k}\; A} \right)}\mspace{14mu}{and}}} & (1) \\{{R_{k} = \frac{L}{k\; A}},} & (2)\end{matrix}$where q_(k) is the heat conduction rate (cal-sec⁻¹ or BTU-hr⁻¹), k isthe thermal conductivity (cal-sec⁻¹-° C.⁻¹-cm⁻¹ or BTU-hr⁻¹-°F.⁻¹-ft⁻¹), A is the cross sectional area of the plate (cm² or ft²), Lis the thickness of the plate (cm or ft), and R_(k) is the conductiveresistance (sec-cal⁻¹-° C. or hr-BTU⁻¹-°F.). Equations (1) and (2) maybe used for representing heat conduction across a delamination gap Lwith one surface at temperature T₁ and the other at temperature T₂.

In some embodiments, such as for a flat plate with a large diameter, theheat convection rate from a surface is given by equations (3) and (4),

$\begin{matrix}{q_{h} - {\frac{T_{surf} - T_{amb}}{\left( {{1/h_{conv}}A} \right)}\mspace{14mu}{and}}} & (3) \\{{R_{h} = \frac{1}{h_{conv}A}},} & (4)\end{matrix}$where T_(surf) is the top surface temperature, T_(amb) is the ambienttemperature of the air contacting the surface, q_(h) is the heatconvection rate (cal-sec⁻¹ or BTU-hr^(−1 ), h) _(conv) is the heatconvection film coefficient (cal-sec⁻¹-° C.⁻¹-cm⁻², BTU-hr⁻¹ F⁻¹-ft⁻² orW-K⁻¹-m⁻²), A is the surface area of the plate(cm², m² or ft²), andR_(h) is the convective resistance (sec-cal⁻¹-° C. or hr-BTU⁻¹-°F.). Fornatural (unforced) convection, a typical value for the heat convectionfilm coefficient is 4 W-K⁻¹-m⁻². Using equations (3)and (4), the heatconvection rate across each side of a delamination air gap with onesurface at temperature T₁ and other surface at temperature T_(2 (T)₁>T₂) is given by equation (5a),

$\begin{matrix}{{q_{h}\frac{T_{1} - T_{amb}}{\left( {{1/h_{conv}}A} \right)}} = \frac{T_{amb} - T_{2}}{\left( {{1/h_{conv}}A} \right)}} & \left( {5a} \right)\end{matrix}$Further, the ambient temperature of the air for thin gaps is given byequation (5b),

$\begin{matrix}{T_{amb} = \frac{T_{1} + T_{2}}{2}} & \left( {5b} \right)\end{matrix}$When the air gap becomes smaller than a threshold value represented asthe Biot number, the amount of heat exchange by convection is replacedby heat conduction. The heat exchange across the boundaries due to theconvection can be assumed to be zero if the Biot number is less than orequal to 0.1 (N_(Bi)=hL/k≦0.1). This relationship gives an expressionfor the threshold air gap thickness as L_(thr)=0.1 k/h. Taking the airconductivity to be 0.026 W/mK and assuming the convection coefficient tobe 5 W/m²K, then a threshold gap thickness of 0.020 inch (0.5 mm) iscalculated, beyond which heat convection is applicable. Heat conductionis present if the gap thickness is less than the threshold gapthickness. The narrowing of the air gap results in increased heatconduction across the air gap, which manifests as a decrease in the peakcontrast value of the void. Loss of the peak contrast value by 20% maynot occur until the gap narrows significantly compared to the thresholdvalue of the gap thickness.

In some embodiments, such as for a flat plate with a large diameter, theradiative heat transfer rate is given by equations (6), (7), and (8),

$\begin{matrix}{{q_{r} = \frac{T_{surf} - T_{refl}}{\left( {{1/h_{r}}A} \right)}},} & (6) \\{{h_{r} = {ɛ\;{\sigma\left( {T_{surf} + T_{refl}} \right)}\left( {T_{surf}^{2} + T_{refl}^{2}} \right)}},\mspace{14mu}{and}} & (7) \\{{R_{r} = \frac{1}{h_{r}A}},} & (8)\end{matrix}$where T_(refl) is the apparent temperature experienced by the objectsurface due to the camera-side background temperature in units of Kelvinor Rankine, T_(amb) is the temperature of the air surrounding the objectin Kelvin or Rankine, σ is the Stefan-Boltzmann Constant 5.670400×10⁻⁸W·m⁻²·K⁻⁴, ε is the emissivity of the test object surface (assuming sameemissivity on top (front) and bottom (rear) surfaces), h_(r) is the heatradiation transfer coefficient (cal-sec⁻¹-° C.⁻¹-cm⁻² or BTU-hr⁻¹-°F.⁻¹-ft⁻²), and R, is the radiative resistance (sec-cal⁻¹-° C. orhr-BTU⁻¹-° F.). At a temperature of 300 K for a 10 K temperaturedifference between the object surface temperature and the correspondingreflection (background) temperature, the radiation transfer coefficientis less than 6 W-K⁻¹-m⁻².

In some embodiments, such as for a large but thin slab of isotropicmaterial with uniform thickness that is exposed to a heat pulse on thefront surface, the resulting one dimensional transient heat transfer isdescribed by equations (9) and (10a),

$\begin{matrix}{\frac{\mathbb{d}T}{\mathbb{d}t} = {{\alpha \cdot \frac{\mathbb{d}^{2}T}{\mathbb{d}z^{2}}}\mspace{14mu}{and}}} & (9) \\{{{T\left( {t = 0} \right)} = T_{\;{in}}},} & \left( {10a} \right)\end{matrix}$where α is the test object (slab) diffusivity (cm²/s), and z is thedistance along the thickness direction. The total heat transfer rate atthe slab surface is given by equation (10b),q=q_(k)+q_(h)+q_(r).  (10b)Neglecting the air emission, the heat flux boundary conditions are givenby equations (11) and (12),

$\begin{matrix}{{- \left( {k \cdot \frac{\mathbb{d}T}{\mathbb{d}z}} \right)_{front}} = {q - {h_{front}\left( {T_{front} - T_{{amb} - {front}}} \right)} - {\sigma\;{ɛ\left( {T_{front}^{4} - T_{{refl} - {front}}^{4}} \right)}}}} & (11) \\{{{- \left( {k \cdot \frac{\mathbb{d}T}{\mathbb{d}z}} \right)_{rear}} = {q - {h_{rear}\left( {T_{rear} - T_{{amb} - {rear}}} \right)} - {\sigma\;{ɛ\left( {T_{rear}^{4} - T_{{refl} - {rear}}^{4}} \right)}}}},} & (12)\end{matrix}$where T(t=0)=T_(in) is the initial steady state temperature of the testobject before the flash and h_(front) and h_(rear) are the convectioncoefficients at the front and rear surfaces, respectively.

In practice, an IR camera measures pixel intensity. Radiometric camerascan measure the surface temperature. Radiometric cameras are not knownto be set-up for compensating the transient surrounding temperature.Radiometric cameras may have input for a constant reflection(background) temperature. They may use a reflective foil to assess thestable reflection temperature. For the exemplary embodiments describedherein, either a radiometric IR camera (i.e. measure apparenttemperature) or an IR camera that measures the irradiance (i.e. measurepixel intensity) may be used because the exemplary embodiments use amethod described herein to capture the transient reflection temperature.The method assumes that camera pixel intensity response is proportionalto the camera irradiance in the desired temperature range.

Considering the definition of the normalized contrast based on the pixelintensity, its relationship with the temperature of the test object willbe derived. The pixel refers to the camera image picture element. Thepixel size refers to the instantaneous field of view (IFOV), which isthe corresponding area of the object surface imaged in the pixel. Aselected pixel grid area, usually in the form of a rectangle, is calledthe image region of interest (ROI, or when plural ROIs). The size of theROI then refers to the area of the object surface imaged in the ROI. Thecorresponding area of the test object is referred to as the object ROI.The camera measures total radiation incident on its detector arrayelement and displays it as a pixel in the image. The detector elementresponse or the pixel intensity registered by the camera is governed bythe following equation (13a),W=W_(obj)+W_(refl)+W_(aim),  (13a)where W is the average pixel intensity due to the heat irradiance(measured in units of W/m², cal-sec⁻¹-cm⁻², or BTU-hr⁻¹-ft⁻²) of thecorresponding camera detector elements from the object ROI measured ingray scale bit value (positive integers). The right hand terms inequation (13a) are given by equations (14), (15), and (16),W_(obj)=ετW′_(obj),  (14)W_(refl)=(1−ε)τW′_(refl), and  (15)W_(atm)=(1−τ)τW′_(atm),  (16)where W_(obj) is the contribution to the pixel intensity due to the heatemission from the object ROI, W_(refl) is the contribution to the pixelintensity due to the heat reflection from the object ROI, and W_(atm) isthe contribution to the pixel intensity due to the heat emission fromthe air between the object ROI and camera. If the method assumes aperfect focus and that the ROI has a uniform temperature at any time,then equations (17), (18), and (19) will apply,W′_(obj)=C_(cam)σT⁴,  (17)W′_(refl)=C_(cam)σT_(refl) ⁴, and  (18)W′_(atm)=C_(cam)σT_(atm) ⁴,  (19)where W′_(obj) is the uncompensated contribution to the pixel intensitydue to the heat emission from the test object ROI, W′_(refl) is theuncompensated contribution to the pixel intensity due to the heatreflection from the test object ROI, W′_(atm) is the uncompensatedcontribution to the pixel intensity due to the heat emission from theair between the camera and object, T is the surface temperature inKelvin or Rankine, T_(refl) is the apparent temperature experienced bythe object surface due to the camera-side background temperature inKelvin or Rankine, T_(atm) is the temperature of the air between thecamera and the object in Kelvin or Rankine, C_(cam)σ is the cameraconstant, ε is the thermal emissivity of the test object surface, and τis the thermal radiation (at camera detection wavelength) transmissivityof the air between the test object and the camera. The thermalemissivity is dependent on the thermal wavelength for a non-gray body.The wavelength spectrum is affected by the surface temperature. Assumingthat the emissivity is high and the test object is a gray body, theemissivity is not dependent on the wavelength. However, the IR camerameasures radiation in a selected band of the wavelength (e.g. 3-5micron). Equations (17), (18), and (19) apply to the total radiationintegrated over all wavelengths. Thus, in reality, in equations (17),(18), and (19), the exponent (or power) of the temperature variable Tmay not be equal to four. The exponent of the temperature variable maybe between 2 to 17. The following analysis is applicable for thesevalues of the exponent.

A calibrated camera provides a linear response with the thermalradiation incident on the detector array element. This relationshipimplies that, in a hypothetical case of absolute zero temperature, ifthe camera calibration is extrapolated, all detector elements shallprovide zero pixel intensity. The method assumes that the cameraconstant is the same within a range of 280 K to 350 K. The pixelintensity or the pixel grayscale value also depends upon the pixel bitresolution (typically 14 bit). The pixel intensity has an uppersaturation limit dictated by the pixel bit resolution. A typical InSbmid-wave camera used in flash thermography operates at a wavelength ofabout 3 to about 5 micron. The transmissivity of air is a function ofthe distance, humidity, air composition, and wavelength. A pronounceddip in the transmissivity occurs at a wavelength of 4.2 micron due toCO₂ absorption. Due to a short distance (˜1 ft) between the camera andthe test object, the contribution of air emission (emissivity˜0) is verysmall and is neglected herein. Correspondingly, the air transmission(transmissivity˜1) is almost 100%. The microbolometer long-wave cameraworks in the 9 to12 micron wavelength and has better air transmissivityeven for longer distances of several feet (e.g. 30 ft). Therefore,equation (13a) can be simplified to equation (13b),W≅W_(obj)+W_(refl).  (13b)

The normalized image contrast is defined based on the pixel intensity asexpressed in equations (20), (21), and (22),

$\begin{matrix}{{{\overset{\_}{C}}_{W}^{t} = \frac{{\Delta\; W} - {\Delta\; W_{ref}}}{{\Delta\; W} + {\Delta\; W_{ref}}}},} & (20) \\{{{\Delta\; W} = {W - W^{0}}},\mspace{14mu}{and}} & (21) \\{{{\Delta\; W_{ref}} = {W_{ref} - W_{ref}^{0}}},} & (22)\end{matrix}$where C _(W) ^(l) is the normalized IR image (pixel intensity) contrast,ΔW is the change in the pixel intensity of the measurement ROI after theflash, W is the pixel intensity at the measurement ROI at the post-flashtime t, W⁰ is the pixel intensity at the measurement ROI before theflash, ΔW_(ref) is the change in the pixel intensity of the referenceROI after the flash, W_(ref) is the pixel intensity at the reference ROIat the post-flash time t, and W_(ref) ⁰ is the pixel intensity at thereference ROI before the flash. The normalized image contrast is alsocalled the normalized irradiance or pixel intensity contrast.

The normalized surface temperature contrast is defined as expressed inequations (23), (24), and (25),

$\begin{matrix}{{{\overset{\_}{C}}^{t} = \frac{{\Delta\; T} - {\Delta\; T_{ref}}}{{\Delta\; T} + {\Delta\; T_{ref}}}},} & (23) \\{{{\Delta\; T_{ref}} = {T_{ref} - T_{ref}^{0}}},\mspace{14mu}{and}} & (24) \\{{{\Delta\; T} = {T - T^{0}}},} & (25)\end{matrix}$where C ^(l) is the normalized flash surface temperature contrast, ΔT isthe change in the surface temperature of the measurement ROI after theflash, T is the surface temperature at the measurement ROI at thepost-flash time t, T⁰ is the surface temperature at the measurement ROIbefore the flash, ΔT_(ref) is the change in the surface temperature ofthe reference ROI after the flash, T_(ref) is the surface temperature atthe reference ROI at the post-flash time t, and T_(ref) ⁰ is the surfacetemperature at the reference ROI before the flash.

The normalized image contrast is related to the normalized temperaturecontrast. As a first approximation, an exemplary embodiment of themethods described herein assumes that the air transmissivity is unitydue to short distance (e.g. 1 ft) and the air heat radiation isnegligible between the object and the camera. Therefore, equation (13a)simplifies to equation (26),W≅εW′_(obj)+(1−ε)W′_(refl).  (26)Substituting equations (17) and (18) into equation (26) results inequation (27),W≅C_(cam)σ(εT⁴+(1−ε)T_(refl) ⁴).  (27)Assuming that the contribution to the pixel intensity from the reflectedtemperature remains the same between the measurement ROI and thereference ROI, the temperature rise at the measurement (object) ROT isrelated to the rise in the pixel intensity at the corresponding imageROI by equations (28) and (29),ΔW≅C_(cam)σ(ε(T⁴−T⁰ ⁴ )+(1−ε)(T_(refl) ⁴−T_(refl) ⁰ ⁴ )), and  (28)ΔW_(ref)≅C_(cam)σ(ε(T_(ref) ⁴−T_(ref) ⁰ ⁴ )+(1−ε)(T_(refl) ⁴−T_(refl) ⁰⁴ )).  (29)Substituting the equations (28) and (29) in the definition of imagecontrast, equation (20), the method arrives at the expression inequation (30),

$\begin{matrix}{{\overset{\_}{C}}_{W}^{t} \cong {\frac{ɛ\left( {\left( {T^{4} - T^{0^{4}}} \right) - \left( {T_{ref}^{4} - T_{ref}^{0^{4}}} \right)} \right)}{\left( {{ɛ\left( {\left( {T^{4} - T^{0^{4}}} \right) + \left( {T_{ref}^{4} - T_{ref}^{0^{4}}} \right)} \right)} + {2\left( {1 - ɛ} \right)\left( {T_{refl}^{4} - T_{refl}^{0^{4}}} \right)}} \right)}.}} & (30)\end{matrix}$If a simulation program, such as the software program sold commerciallyknown as ThermoCalc, is used to generate the temperature evolution atthe measurement and reference ROIs, then equation (30) can be used togenerate the image contrast evolution provided the method estimates thereflection temperature evolution. In practice, the reflectiontemperature changes with time due to cooling of the flash lamps. Thereflected temperature evolution can be estimated based on the measureddata on a high reflectivity foil and a high emissivity tape. With theestimation of the reflected temperature evolution, the expression ofequation (30) can be used to estimate the normalized image contrast.

The estimated image contrast would be partially compensated for thereflection temperature. Only the camera measurement for the reflectiontemperature is compensated. The reflection temperature evolution is ameasure of the heat source (or incident) temperature evolution. The netheat transfer due to the radiation is relatively small. Heat convectionis accounted for in the simulation performed by the ThermoCalc software.The simulation program provides choices for the shape and duration ofthe heat pulse. Depending upon the user's choice, the heat sourcesimulation may or may not model the afterglow or the reflectiontemperature. Thus, if the reflection temperature is not modeled in thesimulation, then the estimation of the image contrast from the simulatedtemperature would he considered to he partially compensated for theafterglow.

Alternatively, a second approach is to increase the convective heattransfer coefficient by the average radiation heat transfer coefficient.The convective heat transfer coefficient is of the order of 5 W/m²K forflash thermography. Although, the radiative heat transfer coefficient isa function of the temperature, it is less than 5 W/m²K for a 10 Kdifference in the temperature range of about 300 K ambient temperature.The radiative heat transfer coefficient can be lumped together with theconvective heat transfer coefficient to a value of 10 W/m²K in thesimulation. This relationship may allow better prediction of the surfacetemperature in the flash thermography using the model and also betterprediction of the image contrast.

Yet another approach is to model the heat source as a high intensitypulse followed by a very low intensity decaying afterglow.

The estimation of the temperature contrast from the IR measurementrequires measurement of the pre-flash surface temperature and themeasurement of pixel intensity of a black tape affixed to the surface ofthe test object. For instance, the method may use a high emissivity(ε>0.95) tape (e.g., tape sold commercially by the 3M Company under theproduct name of 3M 33 or 3M Scotch Brand 235) positioned near the testobject. The emissivity of the tape is assumed to be constant for boththe pre-flash and the post-flash times. The method measures thepre-flash surface temperature of an ROI in the center of the black tapeusing a calibrated radiometric IR camera. The surface temperature needsto be close to the equilibrium or steady state. The method also measuresthe ROI intensity and assumes a high transmissivity value for the air.Thus the pixel intensity due to the tape can be expressed as given inequation (31),W_(tape)=C_(cam)σ((1−ε_(tape))T_(refl) ⁴+ε_(tape)T_(tape) ⁴).  (31)Due to the high emissivity of the tape, equation (31) can be simplifiedto equation (32),W_(tape)≅C_(cam)σ(ε_(tape)T_(tape) ⁴).  (32)If the method measures the pre-flash tape temperature, then the methodcan estimate the camera constant (C′_(cam)) as given in the expressionof equation (33),

$\begin{matrix}{C_{cam}^{\prime} = {{C_{cam}\sigma} \cong {\frac{W_{tape}^{0}}{ɛ_{tape}T_{tape}^{0^{4}}}.}}} & (33)\end{matrix}$Later a more precise expression for the camera constant will be derived.

To measure the T_(refl) or W_(refl), the method introduces a diffusedhigh reflectivity (ε<0.05) reflector such as an aluminum foil that isadequately wrinkled. The emissivity of the foil is assumed to beconstant for both pre-flash and post-flash times. The foil is placedlevel with the object and close to the physical location of themeasurement and reference ROIs, such as on the top surface of the testobject surface. The method can use two foils, one on either side of themeasurement ROI. Here, the method assumes that the reflectiontemperature is uniform over the test object and the foil, as given byequation (34),W_(foil)=C_(cam)σ((1−ε_(foil))T_(refl) ⁴+ε_(foil)T_(foil) ⁴).  (34)The contribution of the foil emission is relatively small compared tothe foil reflection. In the exemplary method, from equation (34), anexpression for the reflection temperature may be written as expressed inequation (35),

$\begin{matrix}{T_{refl}^{4} \cong {\frac{W_{foil} - {{W_{tape}^{0}\left( \frac{ɛ_{foil}}{ɛ_{tape}} \right)}\left( \frac{T_{foil}^{4}}{T_{tape}^{0^{4}}} \right)}}{C_{cam}^{\prime}\left( {1 - ɛ_{foil}} \right)}.}} & (35)\end{matrix}$Also, the exemplary method assumes that the foil temperature is aboutsame as the pre-flash reference temperature due to the contact with thetest object. The black tape is in contact with the test object,therefore the temperature estimations of equation (36) holdT_(foil)≅T_(foil) ⁰≅T_(ref) ⁰≅T_(tape) ⁰.  (36)Equation (35) then simplifies to equation (37a),

$\begin{matrix}{T_{refl}^{4} \cong {\frac{W_{foil} - {W_{tape}^{0}\left( \frac{ɛ_{foil}}{ɛ_{tape}} \right)}}{C_{cam}^{\prime}\left( {1 - ɛ_{foil}} \right)}.}} & \left( {37a} \right)\end{matrix}$The pre-flash reflection temperature may then be expressed by equation(37b),

$\begin{matrix}{T_{refl}^{0^{4}} \cong {\frac{W_{foil}^{0} - {W_{tape}^{0}\left( \frac{ɛ_{foil}}{ɛ_{tape}} \right)}}{C_{cam}^{\prime}\left( {1 - ɛ_{foil}} \right)}.}} & \left( {37b} \right)\end{matrix}$The difference between the fourth power of the reflection temperaturebefore and after the flash is now given by equation (38),

$\begin{matrix}{{T_{refl}^{4} - T_{refl}^{0^{4}}} \cong {\frac{W_{foil} - W_{foil}^{0}}{C_{cam}^{\prime}\left( {1 - ɛ_{foil}} \right)}.}} & (38)\end{matrix}$Knowing the camera constant, equation (38) can be evaluated as afunction of the post-flash time and then substituted in the imagecontrast expression of equation (30). The combined steps of using thehigh reflectivity foil and of using the high emissivity tape is referredto as the “Foil-Tape Method” for the exemplary embodiments describedherein.

The surface temperature evolution data can be obtained using asimulation program such as the previously mentioned ThermoCalc software.The IRFT data acquisition using a radiometric camera that accounts forthe transient reflection temperature can provide the surface temperatureevolution data. Currently, this feature is not available in IR cameras.Here, the exemplary embodiments provide an IR measurement method so thatmeasurement of the transient surface temperature can be performed by theIR radiometric cameras. The change in the pixel intensity at the foilROI may be defined as expressed in equation (39),ΔW_(foil)=W_(foil)−W_(foil) ⁰.  (39)Using equations (30), (38), and (39), the estimated image contrastexpression using the highly reflective foil is given by equation (40),

$\begin{matrix}{{\overset{\_}{C}}_{W}^{t} \cong {\frac{ɛ\left( {\left( {T^{4} - T^{0^{4}}} \right) - \left( {T_{ref}^{4} - T_{ref}^{0^{4}}} \right)} \right)}{{ɛ\left( {\left( {T^{4} - T^{0^{4}}} \right) + \left( {T_{ref}^{4} - T_{ref}^{0^{4}}} \right)} \right)} + {2\frac{\left( {1 - ɛ} \right)\;\Delta\; W_{foil}}{C_{cam}^{\prime}\left( {1 - ɛ_{foil}} \right)}}}.}} & (40)\end{matrix}$A simpler expression for the normalized image contrast will now bederived. From equation (13a), the change in the measurement ROIintensity may be derived as expressed in equation (41),

$\begin{matrix}{{\Delta\; W} = {C_{cam}{{\sigma\begin{bmatrix}{{{ɛ\left( {T - T^{0}} \right)}\left( {T + T^{0}} \right)\left( {T^{2} + T^{0^{2}}} \right)} +} \\{\left( {1 - ɛ} \right)\left( {T_{refl} - T_{refl}^{0}} \right)\left( {T_{refl} + T_{refl}^{0}} \right)\left( {T_{refl}^{2} + T_{refl}^{0^{2}}} \right)}\end{bmatrix}}.}}} & (41)\end{matrix}$

Similarly, the change in the intensity for the reference ROI may beexpressed as in equation (42),

$\begin{matrix}{{\Delta\; W_{ref}} = {C_{cam}{{\sigma\begin{bmatrix}{{{ɛ\left( {T_{ref} - T_{ref}^{0}} \right)}\left( {T_{ref} + T_{ref}^{0}} \right)\left( {T_{ref}^{2} + T_{ref}^{0^{2}}} \right)} +} \\{\left( {1 - ɛ} \right)\left( {T_{refl} - T_{refl}^{0}} \right)\left( {T_{refl} + T_{refl}^{0}} \right)\left( {T_{refl}^{2} + T_{refl}^{0^{2}}} \right)}\end{bmatrix}}.}}} & (42)\end{matrix}$The difference between the change in the measurement ROI intensity andthe change in the reference ROI intensity may be expressed as inequation (43),

$\begin{matrix}{{{\Delta\; W} - {\Delta\; W_{ref}}} = {C_{cam}{{\sigma\begin{bmatrix}{{{ɛ\left( {T - T^{0}} \right)}\left( {T + T^{0}} \right)\left( {T^{2} + T^{0^{2}}} \right)} -} \\{{ɛ\left( {T_{refl} - T_{ref}^{0}} \right)}\left( {T_{ref} + T_{refl}^{0}} \right)\left( {T_{ref}^{2} + T_{ref}^{0^{2}}} \right)}\end{bmatrix}}.}}} & (43)\end{matrix}$The sum of the change in the measurement ROI intensity and the change inthe reference ROI intensity may be expressed as in equation (44),

$\begin{matrix}{{{\Delta\; W} + {\Delta\; W_{ref}}} = {C_{cam}{{\sigma\begin{bmatrix}{{{ɛ\left( {T - T^{0}} \right)}\left( {T + T^{0}} \right)\left( {T^{2} + T^{0^{2}}} \right)} +} \\{{{ɛ\left( {T_{ref} - T_{ref}^{0}} \right)}\left( {T_{ref} + T_{ref}^{0}} \right)\left( {T_{ref}^{2} + T_{ref}^{0^{2}}} \right)} +} \\{2\left( {1 - ɛ} \right)\left( {T_{refl} - T_{refl}^{0}} \right)\left( {T_{refl} + T_{refl}^{0}} \right)\left( {T_{refl}^{2} + T_{refl}^{0^{2}}} \right)}\end{bmatrix}}.}}} & (44)\end{matrix}$Assuming that the difference between the reference and measurementtemperature is small (e.g. <5 K) at the time of maximum contrast, thenthe expression in equation (45) may be shown,

$\begin{matrix}{{\left( {T + T^{0}} \right)\left( {T^{2} + T^{0^{2}}} \right)} \cong {\left( {T_{ref} + T_{ref}^{0}} \right)\left( {T_{ref}^{2} + T_{ref}^{0^{2}}} \right)} \cong {\left( {T_{refl} + T_{refl}^{0}} \right){\left( {T_{refl}^{2} + T_{refl}^{0^{2}}} \right).}}} & (45)\end{matrix}$Therefore, using equations (43) and (44) the expression in equation (46)may be shown,

$\begin{matrix}{\frac{{\Delta\; W} - {\Delta\; W_{ref}}}{{\Delta\; W} + {\Delta\; W_{ref}}} \cong {\frac{\left\lbrack {{ɛ\left( {T - T^{0}} \right)} - {ɛ\left( {T_{ref} - T_{ref}^{0}} \right)}} \right\rbrack}{\left\lbrack {{ɛ\left( {T - T^{0}} \right)} + {ɛ\left( {T_{ref} - T_{ref}^{0}} \right)} + {2\left( {1 - ɛ} \right)\left( {T_{refl} - T_{refl}^{0}} \right)}} \right\rbrack}.}} & (46)\end{matrix}$Using equation (20), equation (46) may be written as expressed inequation (47),

$\begin{matrix}{{{\overset{\_}{C}}_{W}^{t} \cong \frac{ɛ\left( {{\Delta\; T} - {\Delta\; T_{ref}}} \right)}{\left\lbrack {{ɛ\left( {{\Delta\; T} + {\Delta\; T_{ref}}} \right)} + {2\left( {1 - ɛ} \right)\Delta\; T_{refl}}} \right\rbrack}},} & (47)\end{matrix}$where the change in reflection temperature is expressed in equation(48),ΔT_(refl)=(T_(refl)−T_(refl) ⁰).  (48)Therefore, equation (47) may be written as expressed in equation (49),

$\begin{matrix}{{\overset{\_}{C}}_{W}^{t} \cong {\frac{\left( {{\Delta\; T} - {\Delta\; T_{ref}}} \right)}{\left\lbrack {\left( {{\Delta\; T} + {\Delta\; T_{ref}}} \right) + {2\left( {\frac{1}{ɛ} - 1} \right)\Delta\; T_{refl}}} \right\rbrack}.}} & (49)\end{matrix}$Using the definition of the temperature contrast of equation (23), themethod arrives at the normalized image contrast expression of equation(50),

$\begin{matrix}{{\overset{\_}{C}}_{W}^{t} \cong {\frac{{\overset{\_}{C}}^{t}}{\left\lbrack {1 + \frac{2\left( {\frac{1}{ɛ} - 1} \right)\Delta\; T_{refl}}{\left( {{\Delta\; T} + {\Delta\; T_{ref}}} \right)}} \right\rbrack}.}} & (50)\end{matrix}$Next, equation (50) may be rearranged for the normalized temperaturecontrast expressed in equation (51),

$\begin{matrix}{{\overset{\_}{C}}^{t} \cong {\left\lbrack {1 + \frac{2\left( {\frac{1}{ɛ} - 1} \right)\Delta\; T_{refl}}{\left( {{\Delta\; T} + {\Delta\; T_{ref}}} \right)}} \right\rbrack{{\overset{\_}{C}}_{W}^{t}.}}} & (51)\end{matrix}$Thus, the not finalized image (pixel intensity) contrast and thenormalized temperature contrast can be approximately related to eachother. An expression for the normalized pixel intensity contrast tonormalized temperature (or pixel intensity/temperature) contrast ratioε′ may be expressed as given in equation (52),

$\begin{matrix}{{ɛ^{\prime} \cong \frac{1}{\left\lbrack {1 + \frac{2\left( {\frac{1}{ɛ} - 1} \right)\Delta\; T_{refl}}{\left( {{\Delta\; T} + {\Delta\; T_{ref}}} \right)}} \right\rbrack}},} & (52)\end{matrix}$and an expression for the relationship between the normalized imagecontrast and the normalized temperature contrast may be written asexpressed in equation (53),C _(W) ^(l)≅ε^(l) C ^(t).  (53)The pixel/temperature, contrast ratio indicates that the reflectiontemperature rise (caused by flash decay), the object temperature rise(due to the flash power during rise time), and the emissivity affect theconversion between the two contrasts. The reflection temperature is dueto the glass shield and the flash lamps. An estimated amount of lessthan 50% of the flash energy comes through the glass shield of the flashlamps during the flash duration. The remaining energy comes through theglass shield as the flash lamps continue to glow after the flash,providing an increase in the reflection temperature. Similarly, theglass casing of the bulb and the glass shield get hot during the flashand continue to provide thermal radiation. Some flash-hood designs usefans to cool the lamps after the flash to reduce the amount of heat fromafterglow. Assuming that the reflection temperature is the same as theambient temperature immediately after the flash, then equation (53) maybe simplified to the expression in equation (54),C ^(l)≅ C _(W) ^(l).  (54)A shutter that covers the flash lamps immediately after the flash can beused to achieve a constant reflection temperature. In practice,ΔT_(refl) is positive and the image contrast and the temperaturecontrast would differ unless the object has an emissivity value of one.Now, equations to compute temperatures at the measurement ROI and thereference ROI using the measured ROI intensities will be derived. Fromequations (27) and (31), the temperature at the measurement ROI is givenby equation (55a),

$\begin{matrix}{T = {\left( \frac{{\frac{W}{W_{tape}^{0}}ɛ_{tape}{T_{tape}^{0}}^{4}} - {\left( {1 - ɛ} \right){T_{refl}}^{4}}}{ɛ} \right)^{0.25}.}} & \left( {55a} \right)\end{matrix}$In equation (55a), all quantities are known or measured except thereflection temperature. The reflection temperature is derived fromequation (35) and may be expressed as in equation (55b):

$\begin{matrix}{{T_{refl}}^{4} \cong {\frac{W_{foil} - {W_{tape}^{0}\left( \frac{ɛ_{foil}}{ɛ_{tape}} \right)}}{\frac{W_{tape}^{0}}{{T_{tape}^{0}}^{4}}\left( \frac{1 - ɛ_{foil}}{ɛ_{tape}} \right)}.}} & \left( {55b} \right)\end{matrix}$The pre-flash temperature at the measurement ROI is given by equation(56),

$\begin{matrix}{T^{0} = {\left( \frac{{ɛ_{tape}\frac{W^{0}}{W_{tape}^{0}}{T_{tape}^{0}}^{4}} - {\left( {1 - ɛ} \right){T_{refl}^{0}}^{4}}}{ɛ} \right)^{0.25}.}} & (56)\end{matrix}$In equation (56), all quantities are known or measured except thepre-flash reflection temperature, which is given by equation (37b).Similarly, the temperature at the reference ROI is given by equation(57),

$\begin{matrix}{T_{ref} = {\left( \frac{{ɛ_{tape}\frac{W_{ref}}{W_{tape}^{0}}{T_{tape}^{0}}^{4}} - {\left( {1 - ɛ} \right){T_{refl}}^{4}}}{ɛ} \right)^{0.25}.}} & (57)\end{matrix}$Similarly, the pre-flash temperature at the reference ROI is given byequation (58),

$\begin{matrix}{T_{ref}^{0} = {\left( \frac{{ɛ_{tape}\frac{W_{ref}^{0}}{W_{tape}^{0}}{T_{tape}^{0}}^{4}} - {\left( {1 - ɛ} \right){T_{refl}^{0}}^{4}}}{ɛ} \right)^{0.25}.}} & (58)\end{matrix}$Using equation (55a) through equation (58) and equation (23) throughequation (25), the temperature contrast may be computed. Thus, thetemperature contrast may be calculated using the ROI intensity providedby the IR camera. The formula assumes that the half-max width at themeasurement and reference point is at least four times the width of therespective ROIs so that the ROI. intensity provided by the camera isclose to the maximum intensity possible for the given temperature.

The accuracy of the estimation of the temperature contrast from themeasured pixel intensity data is quite sensitive to the value of thesurface emissivity of the test object. In one embodiment, the methodassumes that the emissivity of the measurement ROI and the reference ROIare the same. In another embodiment, the method can either independentlymeasure emissivity or use a recommended value. Another approach todetermine emissivity from the IRFT data taken with the foil and the tapeon the test object starts with the relationship between the pixelintensity and the temperature for the foil and the tape. Using equation(36), the method in one embodiment can represent the pre-flash pixelintensity of the foil and the tape as in equation (59) and equation(60), respectively,W_(foil) ⁰=C_(cam)σ((1−ε_(foil))T_(refl) ⁰ ⁴ +ε_(foil)T_(tape) ⁰ ⁴ )and  (59)W_(tape) ⁰≅C_(cam)σ(ε_(tape)T_(tape) ⁰ ⁴ +(1−ε_(tape))T_(refl) ⁰ ⁴).  (60)Equations (59) and (60) may then be arranged as expressed in equations(61) and (62),

$\begin{matrix}{{\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} \cong {C_{cam}{\sigma\left( {\frac{ɛ_{tape}{T_{tape}^{0}}^{4}}{\left( {1 - ɛ_{tape}} \right)} + {T_{refl}^{0}}^{4}} \right)}}}{and}} & (61) \\{\frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)} = {C_{cam}{{\sigma\left( {{T_{refl}^{0}}^{4} + \frac{ɛ_{foil}{T_{tape}^{0}}^{4}}{\left( {1 - ɛ_{foil}} \right)}} \right)}.}}} & (62)\end{matrix}$Equations (61) and (62) may then be combined. to express equations (63),(64), and (65),

$\begin{matrix}{{{\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} = {C_{cam}{\sigma\left( {\frac{ɛ_{tape}{T_{tape}^{0}}^{4}}{\left( {1 - ɛ_{tape}} \right)} - \frac{ɛ_{foil}{T_{tape}^{0}}^{4}}{\left( {1 - ɛ_{foil}} \right)}} \right)}}},} & (63) \\{{{\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} = {C_{cam}{\sigma\left( {\frac{ɛ_{tape}}{\left( {1 - ɛ_{tape}} \right)} - \frac{ɛ_{foil}}{\left( {1 - ɛ_{foil}} \right)}} \right)}{T_{tape}^{0}}^{4}}},{and}} & (64) \\{{C_{cam}^{\prime}{T_{tape}^{0}}^{4}} = {{C_{cam}\sigma\;{T_{tape}^{0}}^{4}} = {\frac{\left( {\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} \right)}{\left( {\frac{ɛ_{tape}}{\left( {1 - ɛ_{tape}} \right)} - \frac{ɛ_{foil}}{\left( {1 - ɛ_{foil}} \right)}} \right)}.}}} & (65)\end{matrix}$Equation (65) provides a more precise expression for the camera constantdefined in equation (33). Equations (59) and (60) may then be arrangedas expressed in equations (66) and (67),

$\begin{matrix}{{\frac{W_{tape}^{0}}{ɛ_{tape}} \cong {C_{cam}^{\prime}\left( {{T_{tape}^{0}}^{4} + \frac{\left( {1 - ɛ_{tape}} \right){T_{refl}^{0}}^{4}}{ɛ_{tape}}} \right)}}{and}} & (66) \\{\frac{W_{foil}^{0}}{ɛ_{foil}} \cong {{C_{cam}^{\prime}\left( {\frac{\left( {1 - ɛ_{foil}} \right){T_{refl}^{0}}^{4}}{ɛ_{foil}} + {T_{tape}^{0}}^{4}} \right)}.}} & (67)\end{matrix}$Equations (66) and (67) may then be combined and expressed as inequation (68),

$\begin{matrix}{{\frac{W_{tape}^{0}}{ɛ_{tape}} - \frac{W_{foil}^{0}}{ɛ_{foil}}} \cong {C_{cam}{{\sigma\left( {\frac{\left( {1 - ɛ_{tape}} \right){T_{refl}^{0}}^{4}}{ɛ_{tape}} - \frac{\left( {1 - ɛ_{foil}} \right){T_{refl}^{0}}^{4}}{ɛ_{foil}}} \right)}.}}} & (68)\end{matrix}$Equations (64) and (68) may then be combined and expressed as inequations (69) and (70),

$\begin{matrix}{\frac{\left( {\frac{W_{tape}^{0}}{ɛ_{tape}} - \frac{W_{foil}^{0}}{ɛ_{foil}}} \right)}{\left( {\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} \right)} \cong \;{\frac{\left( {\frac{\left( {1 - ɛ_{tape}} \right)}{ɛ_{tape}} - \frac{\left( {1 - ɛ_{foil}} \right)}{ɛ_{foil}}} \right)}{\left( {\frac{ɛ_{tape}}{\left( {1 - ɛ_{tape}} \right)} - \frac{ɛ_{foil}}{\left( {1 - ɛ_{foil}} \right)}} \right)}\frac{{T_{refl}^{0}}^{4}}{{T_{tape}^{0}}^{4}}\mspace{20mu}{and}}} & (69) \\{\frac{\left( {\frac{W_{tape}^{0}}{ɛ_{tape}} - \frac{W_{foil}^{0}}{ɛ_{foil}}} \right)}{\left( {\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} \right)} \cong {{- \frac{\left( {1 - ɛ_{tape}} \right)}{ɛ_{tape}}}\frac{\left( {1 - ɛ_{foil}} \right)}{ɛ_{foil}}{\frac{{T_{refl}^{0}}^{4}}{{T_{tape}^{0}}^{4}}.}}} & (70)\end{matrix}$Next, equation (70) may be rearranged and a quantity J may expressed asin equation (71),

$\begin{matrix}{J = {\frac{{T_{refl}^{0}}^{4}}{{T_{tape}^{0}}^{4}} = {\frac{\left( {\frac{W_{tape}^{0}}{ɛ_{tape}} - \frac{W_{foil}^{0}}{ɛ_{foil}}} \right)}{\left( {\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} \right)\left( {{- \frac{\left( {1 - ɛ_{tape}} \right)}{ɛ_{tape}}}\frac{\left( {1 - ɛ_{foil}} \right)}{ɛ_{foil}}} \right)}.}}} & (71)\end{matrix}$Further, a quantity B may be denoted as expressed in equation (72),

$\begin{matrix}{B = {\frac{\left( {\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} \right)}{\left( {\frac{ɛ_{tape}}{\left( {1 - ɛ_{tape}} \right)} - \frac{ɛ_{foil}}{\left( {1 - ɛ_{foil}} \right)}} \right)}.}} & (72)\end{matrix}$Equations (65) and (72) may then be combined and expressed as inequation (73),B=C′_(cam)T_(tape) ⁰ ⁴ .  (73)The camera constant is given by the representation in equation (74),

$\begin{matrix}{C_{cam}^{\prime} = {\frac{\left( {\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} \right)}{\left( {\frac{ɛ_{tape}}{\left( {1 - ɛ_{tape}} \right)} - \frac{ɛ_{foil}}{\left( {1 - ɛ_{foil}} \right)}} \right)}{\frac{1}{{T_{tape}^{0}}^{4}}.}}} & (74)\end{matrix}$The pre-flash temperature at the measurement ROI is given by equation(75),W⁰≅C_(cam)σ(εT⁰ ⁴ +(1−ε)T_(refl) ⁰ ⁴ ).  (75)Due to some noted observations and assumptions, including contact of thetape with the test object, the steady state of surface temperaturebefore flash, and the reflection temperature not differing more than 5 Kfrom the test object temperature before flash, it may be presumed thatequation (76) holdsT⁰≅T_(tape) ⁰.  (76)Equation (76) may then be substituted into equation (75), resulting inthe expressions of equations (77), (78), (79), and (80),

$\begin{matrix}{{W^{0} \cong {C_{cam}{\sigma\left( {{ɛ\;{T_{tape}^{0}}^{4}} + {\left( {1 - ɛ} \right){T_{refl}^{0}}^{4}}} \right)}}},} & (77) \\{{W^{0} \cong {C_{cam}\sigma\;{{T_{tape}^{0}}^{4}\left( {ɛ + {\left( {1 - ɛ} \right)\frac{{T_{refl}^{0}}^{4}}{{T_{tape}^{0}}^{4}}}} \right)}}},} & (78) \\{{W^{0} \cong {B\left( {ɛ + {\left( {1 - ɛ} \right)J}} \right)}},{and}} & (79) \\{ɛ \cong {\frac{\frac{W^{0}}{B} - J}{1 - J}.}} & (80)\end{matrix}$Thus, the emissivity of the test object at the room temperature can beestimated by an embodiment described herein. If the measurement is doneat two different ambient temperatures that are at least 5 K apart, themethod may provide better confidence in the average emissivitymeasurement.

This example illustrates the steps for converting the normalized imagecontrast from the thermography data to the normalized temperaturecontrast using additional measurements required for determining thereflection temperature. In one embodiment, the test object may compriseback-drilled elongated flat bottom slots or holes at various depths.FIG. 3 shows the IRFT image of a test object that is made of reinforcedcarbon-carbon (RCC) with back drilled flat bottom slots and with foiland tape (post-flash time=0.6 sec). The method in this example isinterested in a measurement on the center slot. The locations of themeasurement and reference ROIs are indicated in FIG. 3. One piece of thewrinkled aluminum foil is placed on the left side of the test object andthe other piece of an identical foil is placed on the right side of thetest object. The locations of the foil ROT are indicated. A highemissivity adhesive tape is affixed at the top of the test object. Thetape ROI is indicated in FIG. 3. The image frame time is extremely closeto the peak contrast time. The image indicates normalized pixelintensity. The image display of the contrast is adjusted by manipulatingthe display rectangle location and size. In this example, themeasurement ROI is a single pixel (or simply 1×1 pixel). The sizes ofthe ROIs are provided in the Table I. A 1×1 pixel in dimensions is equalto 0.023 in.×0.023 in. Normally, ROI cursors and lines have colors forquick identification, but colors are not necessary in this description.

TABLE I Pixel Size of Region of Interests Region of Interest Pixel SizeMeasurement 1 × 1 Reference 3 × 3 Foil 2 15 × 15 Foil 1 15 × 15 Tape 9 ×9

The dashed cross lines of FIG. 3 are used to plot the pixel intensityalong the lines to locate the peak point and the baseline intensity forthe selection of the measurement and reference ROIs. FIG. 4 shows a plotof pixel intensity along the horizontal pixel line taken in a frame atpost-flash time of 0.6 seconds. Various ROIs, such as the foil,measurement, and reference ROI, are also identified in FIG. 4.

Table II gives the pre-flash measurements and emissivity inputs. Notethat the representation of Eq. (80) is applied to the Table II data(except for the test object emissivity). The test object emissivity inthis example is estimated to be 0.75 at the measurement ROI. Asignificant number of such measurements would improve confidence in thevalue. Therefore, the method may instead use an emissivity value of0.78, which is the value published in the literature for the objectmaterial.

TABLE II Pre-flash Measurements and Emissivity Inputs T_(refl) ⁰ (K) 300T_(tape) ⁰ (K) 296 ε_(tape) 0.99 ε_(foil) 0.05 ε 0.78 W_(tape) ⁰(average bit value) 6382 W_(foil) ⁰ (average bit value) 6768 W_(ref) ⁰(average bit value) 6480

FIG. 5 provides plots of the pixel intensity evolutions of the two foilROIs. The vertical dotted line at time equal to 0.6 seconds indicatesthe peak contrast time. The foils are reflective but specularreflectivity is undesirable. Moreover, the test object is also diffuselyreflective. The two foils provide two independent measurements of thepixel intensity evolution. The two intensity evolutions agree with eachother and an average value is chosen. The two foils are on either sideof the measurement/reference ROI. Thus, an average of the two foilintensity evolutions provides an estimate of foil intensity evolution inthe measurement/reference ROI with better confidence as opposed tochoosing a single foil intensity evolution.

FIG. 6 shows the pixel intensity evolution at the tape ROI. The flashduration is set to 0.003 seconds. The time between the image frames is0.017 seconds for a frame rate of 60 frames/second. The intensity decaysquite rapidly before the capture of the first post-flash frame. The testobject reaches the maximum temperature at the end of the flash duration,but the camera is incapable of capturing the corresponding peakintensity due to the slow frame rate. FIG. 6 indicates that thetemperature rise is higher on the tape ROI than that on the foil ROI.The tape ROI is in the area of tape overhang and indicates similarintensity evolution as that of the foil ROI.

FIG. 7 shows the pixel intensity evolution at the measurement (uppercurve) and the reference (lower curve) ROI. FIG. 7 indicates the hotspot (higher intensity) of the measurement ROI in comparison to thereference ROI. The two traces for the measurement ROI and the referenceROI eventually merge together as the temperature of the indication areaand the surrounding area become equal.

FIG. 8 shows a plot of a simple image contrast, which is defined as thedifference between the intensities of measurement and reference ROIs.The simple contrast evolution at the measurement ROI indicates a peaktime of approximately 0.5 seconds.

Referring now to FIG. 9, this embodiment begins with equation (65) beingused to compute the camera constant. Next, equations (37a) and (37b) areused to compute the reflection temperature evolution. FIG. 9 provides anexample of a computed reflection temperature evolution. The pre-flashreflection temperature is estimated to be about 305 K, which is 5 Kabove the pre-flash temperature of the test object. Also, the reflectiontemperature is 2 K higher than the pre-flash reflection temperature.When the data for this example was taken, the setup was used to acquirefive other shots within 5 minutes before this represented shot, and thetime between the last shot and die current one was less than a minute.Thus, the flash lamps were warmer than the ambient temperature beforethe flash and caused the reflection temperature to be higher than theambient temperature. In at least one of the embodiments describedherein, the method computes the measurement temperature evolution usingequation (55a). Using equation (57), the method also computes thereference temperature evolution. The three estimated temperatureevolutions are shown together in FIG. 10. The upper curve is for thereflection temperature. The middle curve is for the measurement ROItemperature and the lower curve is for the reference ROI temperature,FIG. 11( a) shows the image contrast computed using the pixel intensityand one fourth (1/4^(th)) power of pixel intensity to illustrateequation (45), which suggests that the contrast computed with the fourthpower of the temperature and the contrast computed with unity power ofthe temperature are approximately the same. FIG. 11( b) demonstrates theestimated temperature contrast (upper curve) along with the imagecontrast (lower curve) with ε=0.78. Thus, the pixel and temperaturecontrast differ, if the test object's emissivity is less than one. FIG.11( b) also illustrates the difference in the peak contrasts due tolower values of the emissivity. FIG. 12 shows an exemplary screen shotof the steps of computing the temperature contrast evolution (uppercurve) and pixel (image) contrast evolution (lower curve) with softwareimplementing the IR Contrast method which relates the thermalmeasurements in terms of the normalized anomaly contrast as a functionof the frame number. FIG. 13 represents the plot of the contrast ratioε′. Two plots are shown. One plot (lower curve) uses the representationgiven by equation (52). The other plot is the ratio of the two contrastsshown in FIG. 12. The plots differ slightly at early instances of time,but the two values agree well at later times. The contrast ratio isapproximately the same as the emissivity of the test object for longertimes when the rate of change in the surface temperature is relativelylow.

In at least one embodiment, the method estimates the normalized imagecontrast based on results from the surface temperature simulation of thesoftware sold commercially as ThermoCalc in order to understand theeffect of the reflection temperature on the profile of the pixelcontrast. In this particular example, the method takes a samplesimulation temperature evolution at the measurement and reference areas.The simulation power input is 1.8E6 W/m^2with a duration setting at0.003 second. This set-up assumes about 30% efficiency for convertingthe electrical power (12 kJ source) to the absorbed energy. Dependingupon the flash power setting, the reflection temperature evolution isaffected. The method of this example estimates the reflectiontemperature evolution based on the experimental method explained in thisdescription.

FIG. 14 shows the simulated temperature evolutions with an assumedreflection temperature evolution. The upper curve represents thereflection temperature. The middle curve is indicative of themeasurement ROI temperature and the lower curve is for the reference ROItemperature. The normalized temperature contrast is calculated using therepresentation given by equation (51). The method of this particularexample assumes that the emissivity of the test object equals 0.78.Using equation (30), the method of this example can compute the imagecontrast. The results are shown in FIG. 15. The upper curve shows thetemperature contrast. The lower curve shows the image contrast. Usingequation (27), the pixel intensity can be determined if the cameraconstant is known. Thus, this example illustrates the influence of theemissivity change on the pixel contrast. It also suggests that changesin the pulse power have a small influence on the pixel contrast due tochanges in the reflection temperature.

If the method of this particular embodiment assumes that one can inputthe ambient reflection temperature in the simulation model, then theafterglow of the heat source would be due to differences in theradiation between the pre-flash and post-flash reflection temperature.The afterglow flux may be represented by equation (81),S_(postflash)=σ(T_(refl) ⁴−T_(refl) ⁰ ⁴ ).  (81)

The afterglow flux evolution starts from the first post-flash frame. Theflash lamp pulse flux evolution is estimated for a duration between thestart of the flash and the first post-flash frame. An example ofafterglow flux evolution is given in FIG. 16. FIG. 17 shows an exampleof flash flux evolution until the first post-flash frame. The flash lamppulse and the post-flash afterglow evolutions can he added to model thecompound source flux evolution for the entire time of data acquisition.

FIG. 18 is a flow diagram illustrating methods for converting an imagecontrast evolution of an object to a temperature contrast evolution, formodeling afterglow flux, and for assessing the test object emissivity,in accordance with some embodiments described herein. Processing beginsat step 1800 whereupon, at block 1805, a steady state temperaturemeasurement is made of the tape affixed to the test object before theflash or the application of heat. At block 1810, the transientthermography IR digital video data of the object, foil, and tape iscollected. The collection of data begins before the application of heat.At block 1815, the pixel intensity evolutions at the measurement,reference, tape, and foil ROIs are measured. At block 1820, thenormalized pixel intensity (image) contrast evolution is computed usingequation (20). At block 1825, the camera constant is computed usingequation (65) and the reflection temperature evolution is computed usingequation (37). At block 1830, the measurement temperature evolution iscomputed using equation (55a) and the reference temperature evolution iscomputed using equation (57). At block 1835, the normalized temperaturecontrast evolution computed using equation (23) or equation (51). Atblock 1840, the afterglow flux is modeled using equation (81). At block1845, the test object emissivity is assessed using equation (80).Processing subsequently ends at step 1899.

FIG. 19 is a flow diagram illustrating a method for converting atemperature contrast evolution of an object to an image contrastevolution, in accordance with some embodiments. Processing begins atstep 1900 whereupon either, at block 1905, the source flux and thereflection temperature evolution are assumed, or at block 1910, thesource flux is based on the heat source setting and modeled from theexperimental reflection temperature evolution using equation (81). Atblock 1915, the transient thermography surface temperature on avoid-like flaw in a selected material is simulated. At block 1920, themeasurement ROI temperature evolution and the reference ROI temperatureevolution are simulated. At block 1925, the normalized temperaturecontrast evolution is computed using equation (23), followed by block1930 where the normalized pixel intensity contrast evolution is computedusing equation (30) or equation (50). Alternatively, at block 1935, thecamera constant is calculated from equation (33) and the change in pixelintensity evolution at the measurement ROI and the reference ROI arecomputed using equation (28) and equation (29), respectively, followedby block 1940 where the normalized pixel intensity contrast evolution iscomputed using equation (20). Processing subsequently ends at step 1999.

The normalized image contrast and the normalized temperature contrastdiffer for objects with emissivity other than one. Therefore, foraccurate results, the embodiments and examples described herein indicatethat the two quantities should not be treated as the same. To comparethe simulation temperature contrast with the measured pixel contrast,the method of the embodiments described herein should estimate theevolution of the reflection temperature and the incident heat flux.Ideally, the set of instructions from a computer software program thatimplements the methods described herein should model the compound heatsource flux evolution, which also includes the thermal afterglow. Theeffect of the reflection temperature on the pixel intensity should alsobe accounted for to seek a better estimation of the temperature contrastevolution from the pixel intensity evolution data.

As described herein, the reflection temperature evolution is establishedbased on data acquired by the IRFT data acquisition system. This systemacquires readings from a test object, a high emissivity tape with knownemissivity, and a diffuse highly reflective metal foil with knownreflectivity. The method also records the steady state pre-flashtemperature of the object using a thermocouple (or other contact sensor)or an accurate radiometer. The IR datacube is recorded using the normalIRFT technique.

The method comprises four regions of interests (ROIs). One region is forthe measurement ROI. The second region is for the reference ROI. Thethird region is the foil ROI for measurement of the reflectiontemperature. The fourth region is for measurement of the pre- flashtemperature at the high emissivity tape.

Using formulas described previously herein, the method estimates thereflection temperature evolution. The method then computes thetemperature contrast from the IRFT data. In accordance with at least oneembodiment described herein, the pixel intensity/temperature contrastratio has been defined in order to relate the temperature contrast tothe image contrast.

The embodiments described herein also include a method for using theevolution of the reflection temperature to model the afterglow flux ofthe flash source. Using the estimated compound source evolution insimulation software, the temperature contrast evolution may be estimatedand then the image contrast profiles on the simulated voids may beestimated.

The embodiments described herein include an emissivity estimationtechnique using the same IR camera that is used in an IRFT system. Thismethod provides determination of the emissivity for the desired thermalwavelength. By using the foil-tape technique during the IRFT shot, thetransient reflection temperature or the reflection temperature evolutioncan be recorded. If an IR camera is programmed with the representativeformulas for reflection temperature formulas described herein, thecamera can provide the object surface temperature directly, even duringthe IRFT data acquisition. The IR camera can also be programmed toestimate the object emissivity in real-time by using the formulasdescribed herein in combination with the set-up described for thefoil-tape technique.

In light of the principles and exemplary embodiments described andillustrated herein, it will be recognized that the exemplary embodimentscan be modified in arrangement and detail without departing from suchprinciples. Also, the foregoing discussion has focused on particularembodiments, but other configurations are contemplated. In particular,even though expressions such as “in one embodiment,” “in anotherembodiment,” or the like are used herein, these phrases are meant togenerally reference embodiment possibilities, and are not intended tolimit the invention to particular embodiment configurations. As usedherein, these terms may reference the same or different embodiments thatare combinable into other embodiments.

Similarly, although exemplary processes have been described with regardto particular operations performed in a particular sequence, numerousmodifications could be applied to those processes to derive numerousalternative embodiments of those described herein. For example,alternative embodiments may include processes that use fewer than all ofthe disclosed operations, processes that use additional operations, andprocesses in which the individual operations disclosed herein arecombined, subdivided, rearranged, or otherwise altered.

In view of the wide variety of useful permutations that may be readilyderived from the example embodiments described herein, this detaileddescription is intended to be illustrative only, and should not be takenas limiting the scope of the invention. What is claimed as theinvention, therefore, are all implementations that come within the scopeof the following claims, and all equivalents to such implementations. Inthe claims, means-plus-function and step-plus- function clauses areintended to cover the structures or acts described herein as performingthe recited function and not only structural equivalents, but alsoequivalent structures. Thus, while a nail and a screw may not bestructural equivalents in that a nail employs a cylindrical surface tosecure wooden parts together, whereas a screw employs a helical surface,in the environment of fastening wooden parts, a nail and a screw may beequivalent structures.

The invention claimed is:
 1. An apparatus for converting an imagecontrast evolution of an object to a temperature contrast evolution, theapparatus comprising: one or more processors; and one or more memoryunits coupled to the processors, the apparatus being configured to:calculate a measurement region of interest temperature change ΔT;calculate a reference region of interest temperature change ΔT_(ref);calculate a reflection temperature change ΔT_(refl); calculate the imagecontrast evolution C _(W) ^(l); and convert the image contrast evolutionto the temperature contrast evolution C ^(l) according to the equationof:${\overset{\_}{C}}^{t} \cong {\left\lbrack {1 + \frac{2\left( {\frac{1}{ɛ} - 1} \right)\Delta\; T_{refl}}{\left( {{\Delta\; T} + {\Delta\; T_{ref}}} \right)}} \right\rbrack{\overset{\_}{C}}_{W}^{t}}$wherein ε is the emissivity of the object.
 2. The apparatus of claim 1further comprising: an IR camera operatively connected to the one ormore processors.
 3. The apparatus of claim 2 wherein the apparatus isfurther configured to measure and display the object surface temperaturein real-time.
 4. The apparatus of claim 2 further comprising: dataacquisition electronics coupled to the IR camera; a flash lamp; a powersupply/trigger unit coupled to the flash lamp; and a computer interfacedwith the power supply/trigger unit and the data acquisition electronics,the computer being configured to trigger the flash lamp and initiatedata acquisition.
 5. The apparatus of claim 4 further comprising: a testobject positioned at the focus of the IR camera; a fell attached to thesurface of the test target; and a tape attached to the surface of thetest target.
 6. An apparatus for converting an image contrast evolutionof an object to a temperature contrast evolution, the apparatuscomprising: one or more processors; and one or more memory units coupledto the processors, the apparatus being configured to: calculate ameasurement region of interest temperature change ΔT; calculate areference region of interest temperature change ΔT_(ref); calculate areflection temperature change ΔT_(refl); calculate the image contrastevolution C _(W) ^(l); and convert the image contrast evolution to thetemperature contrast evolution where the apparatus being configured tocalculate the image contrast evolution comprises: measuring ameasurement region of interest temperature T; measuring a referenceregion of interest temperature T_(ref); measuring a reflectiontemperature T_(refl); and calculating the image contrast evolutionaccording to the equation of:${\overset{\_}{C}}_{W}^{t} \cong \frac{ɛ\left( {\left( {T^{4} - T^{0^{4}}} \right) - \left( {T_{ref}^{4} - {T_{ref}^{0}}^{4}} \right)} \right)}{\left( {{ɛ\left( {\left( {T^{4} - T^{0^{4}}} \right) + \left( {T_{ref}^{4} - {T_{ref}^{0}}^{4}} \right)} \right)} + {2\left( {1 - ɛ} \right)\left( {T_{refl}^{4} - {T_{refl}^{0}}^{4}} \right)}} \right)}$wherein ε is the emissivity of the object, t⁰ is the measurement regionof interest temperature at time of flash, T_(ref) ⁰ is the referenceregion of interest temperature at time of flash, and T_(refl) ⁰ is thereflection temperature at time of flash.
 7. An apparatus for convertingan image contrast evolution of an object to a temperature contrastevolution, the apparatus comprising: one or more processors; and one ormore memory units coupled to the processors; the apparatus beingconfigured to: calculate a measurement region of interest temperaturechange ΔT; calculate a reference region of interest temperature changeΔT_(ref); calculate a reflection temperature change ΔT_(refl); calculatethe image contrast evolution C _(W) ^(l); and convert the image contrastevolution to the temperature contrast evolution, where the apparatusbeing configured to calculate the image contrast evolution comprisescomponents configured and arranged for: measuring a measurement regionof interest temperature T; measuring a reference region of interesttemperature T_(ref); measuring a reflection region of interest pixelintensity W_(foil); calculating a camera constant C′_(com); andcalculating the image contrast according to the equation of:${\overset{\_}{C}}_{W}^{t} \cong \frac{ɛ\left( {\left( {T^{4} - T^{0^{4}}} \right) - \left( {T_{ref}^{4} - {T_{ref}^{0}}^{4}} \right)} \right)}{{ɛ\left( {\left( {T^{4} - T^{0^{4}}} \right) + \left( {T_{ref}^{4} - {T_{ref}^{0}}^{4}} \right)} \right)} + {2\frac{\left( {1 - ɛ} \right)\left( {W_{foil} - W_{foil}^{0}} \right)}{C_{cam}^{\prime}\left( {1 - ɛ_{foil}} \right)}}}$wherein ε is the emissivity of the object, ε_(foil) is the emissivity ofa foil, T⁰ is the measurement region of interest temperature at time offlash, T_(ref) ⁰ is the reference region of interest temperature at timeof flash, and W_(foil) ⁰ is the reflection region of interest pixelintensity at time of flash.
 8. The apparatus of claim 7, where thecamera constant is calculated according to the equation of:$C_{cam}^{\prime} = {\frac{\left( {\frac{W_{tape}^{0}}{\left( {1 - ɛ_{tape}} \right)} - \frac{W_{foil}^{0}}{\left( {1 - ɛ_{foil}} \right)}} \right)}{\left( {\frac{ɛ_{tape}}{\left( {1 - ɛ_{tape}} \right)} - \frac{ɛ_{foil}}{\left( {1 - ɛ_{foil}} \right)}} \right)}\frac{1}{{T_{tape}^{0}}^{4}}}$wherein ε_(tape) is the emissivity of the tape, T_(tape) ⁰ is the taperegion of interest temperature at time of flash, and W_(tape) ⁰ is thetape region of interest pixel intensity at time of flash.
 9. Anapparatus for converting a temperature contrast evolution of an objectto an image contrast evolution, the apparatus comprising: one or moreprocessors; and one or more memory units coupled to the processors, theapparatus being configured to: calculate a measurement region ofinterest temperature change ΔT; calculate a reference region of interesttemperature change ΔT_(ref); calculate a reflection temperature changeΔT_(refl); calculate the temperature contrast evolution C ^(l); andconvert the temperature contrast evolution to the image contrastevolution, where the apparatus being configured to convert thetemperature contrast evolution to the image contrast evolution C _(W)^(l) is calculated according to the equation of:${\overset{\_}{C}}_{W}^{t} \cong \frac{{\overset{\_}{C}}^{t}}{\left\lbrack {1 + \frac{2\left( {\frac{1}{ɛ} - 1} \right)\Delta\; T_{refl}}{\left( {{\Delta\; T} + {\Delta\; T_{ref}}} \right)}} \right\rbrack}$wherein ε is the emissivity of the object.
 10. The apparatus of claim 9further comprising: an IR camera operatively connected to the one ormore processors.
 11. The apparatus of claim 10 wherein the apparatus isfurther configured to measure and display the object surface temperaturein real-time.
 12. The apparatus of claim 10 further comprising: dataacquisition electronics coupled to the IR camera; a flash lamp; a powersupply/trigger unit coupled to the flash lamp; and a computer interfacedwith the power supply/trigger unit and the data acquisition electronics,the computer being configured to trigger the flash lamp and initiatedata acquisition.
 13. The apparatus of claim 12 further comprising: afoil for attachment to the surface of the object; and a tape of knownemissivity for attachment to the surface of the object.
 14. An apparatusfor converting a temperature contrast evolution of an object to an imagecontrast evolution, the apparatus comprising: one or more processors;and one or more memory units coupled to the processors, the apparatusbeing configured to: calculate a measurement region of interesttemperature change ΔT; calculate a reference region of interesttemperature change ΔT_(ref); calculate a reflection temperature changeΔT_(refl); calculate the temperature contrast evolution C ^(l); andconvert the temperature contrast evolution to the image contrastevolution, where the apparatus being configured to calculate thetemperature contrast evolution comprises components configured andarranged for: measuring a measurement region of interest pixel intensityW; measuring a reference region of interest pixel intensity W_(ref);measuring a tape region of interest pixel intensity W_(tape); measuringa reflection temperature T_(refl); and calculating the temperaturecontrast evolution according to equation of:${\overset{\_}{C}}^{\prime} = \frac{{\Delta\; T} - {\Delta\; T_{ref}}}{{\Delta\; T} + {\Delta\; T_{ref}}}$Δ T = T − T⁰ wherein${{\Delta\; T_{ref}} = {T_{ref} - T_{ref}^{0}}},{T = \left( \frac{{\frac{W}{W_{tape}^{0}}ɛ_{tape}{T_{tape}^{0}}^{4}} - {\left( {1 - ɛ} \right){T_{refl}}^{4}}}{ɛ} \right)^{0.25}},{T^{0} = \left( \frac{{ɛ_{tape}\frac{W^{0}}{W_{tape}^{0}}{T_{tape}^{0}}^{4}} - {\left( {1 - ɛ} \right){T_{refl}^{0}}^{4}}}{ɛ} \right)^{0.25}},{T_{ref} = \left( \frac{{ɛ_{tape}\frac{W_{ref}}{W_{tape}^{0}}{T_{tape}^{0}}^{4}} - {\left( {1 - ɛ} \right){T_{refl}}^{4}}}{ɛ} \right)^{0.25}},{{{and}\mspace{14mu} T_{ref}^{0}} = \left( \frac{{ɛ_{tape}\frac{W_{ref}^{0}}{W_{tape}^{0}}{T_{tape}^{0}}^{4}} - {\left( {1 - ɛ} \right){T_{refl}^{0}}^{4}}}{ɛ} \right)^{0.25}},$wherein ε is the emissivity of the object, e_(tape) is the emissivity ofthe tape, T_(tape) ⁰ is the tape region of interest temperature at timeof flash, T_(refl) ⁰ is the reflection temperature at time of flash,W_(ref) ⁰ is the reference region of interest pixel intensity at time offlash, and W_(tape) ⁰ is the tape region of interest pixel intensity attime of flash.